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------------------------------------------------------------------------------ -- -- -- GNAT RUN-TIME COMPONENTS -- -- -- -- ADA.NUMERICS.GENERIC_COMPLEX_ARRAYS -- -- -- -- S p e c -- -- -- -- This specification is derived from the Ada Reference Manual for use with -- -- GNAT. In accordance with the copyright of that document, you can freely -- -- copy and modify this specification, provided that if you redistribute a -- -- modified version, any changes that you have made are clearly indicated. -- -- -- ------------------------------------------------------------------------------ with Ada.Numerics.Generic_Real_Arrays, Ada.Numerics.Generic_Complex_Types; generic with package Real_Arrays is new Ada.Numerics.Generic_Real_Arrays (<>); use Real_Arrays; with package Complex_Types is new Ada.Numerics.Generic_Complex_Types (Real); use Complex_Types; package Ada.Numerics.Generic_Complex_Arrays is pragma Pure (Generic_Complex_Arrays); -- Types type Complex_Vector is array (Integer range <>) of Complex; type Complex_Matrix is array (Integer range <>, Integer range <>) of Complex; -- Subprograms for Complex_Vector types -- Complex_Vector selection, conversion and composition operations function Re (X : Complex_Vector) return Real_Vector; function Im (X : Complex_Vector) return Real_Vector; procedure Set_Re (X : in out Complex_Vector; Re : Real_Vector); procedure Set_Im (X : in out Complex_Vector; Im : Real_Vector); function Compose_From_Cartesian (Re : Real_Vector) return Complex_Vector; function Compose_From_Cartesian (Re, Im : Real_Vector) return Complex_Vector; function Modulus (X : Complex_Vector) return Real_Vector; function "abs" (Right : Complex_Vector) return Real_Vector renames Modulus; function Argument (X : Complex_Vector) return Real_Vector; function Argument (X : Complex_Vector; Cycle : Real'Base) return Real_Vector; function Compose_From_Polar (Modulus, Argument : Real_Vector) return Complex_Vector; function Compose_From_Polar (Modulus, Argument : Real_Vector; Cycle : Real'Base) return Complex_Vector; -- Complex_Vector arithmetic operations function "+" (Right : Complex_Vector) return Complex_Vector; function "-" (Right : Complex_Vector) return Complex_Vector; function Conjugate (X : Complex_Vector) return Complex_Vector; function "+" (Left, Right : Complex_Vector) return Complex_Vector; function "-" (Left, Right : Complex_Vector) return Complex_Vector; function "*" (Left, Right : Complex_Vector) return Complex; function "abs" (Right : Complex_Vector) return Complex; -- Mixed Real_Vector and Complex_Vector arithmetic operations function "+" (Left : Real_Vector; Right : Complex_Vector) return Complex_Vector; function "+" (Left : Complex_Vector; Right : Real_Vector) return Complex_Vector; function "-" (Left : Real_Vector; Right : Complex_Vector) return Complex_Vector; function "-" (Left : Complex_Vector; Right : Real_Vector) return Complex_Vector; function "*" (Left : Real_Vector; Right : Complex_Vector) return Complex; function "*" (Left : Complex_Vector; Right : Real_Vector) return Complex; -- Complex_Vector scaling operations function "*" (Left : Complex; Right : Complex_Vector) return Complex_Vector; function "*" (Left : Complex_Vector; Right : Complex) return Complex_Vector; function "/" (Left : Complex_Vector; Right : Complex) return Complex_Vector; function "*" (Left : Real'Base; Right : Complex_Vector) return Complex_Vector; function "*" (Left : Complex_Vector; Right : Real'Base) return Complex_Vector; function "/" (Left : Complex_Vector; Right : Real'Base) return Complex_Vector; -- Other Complex_Vector operations function Unit_Vector (Index : Integer; Order : Positive; First : Integer := 1) return Complex_Vector; -- Subprograms for Complex_Matrix types -- Complex_Matrix selection, conversion and composition operations function Re (X : Complex_Matrix) return Real_Matrix; function Im (X : Complex_Matrix) return Real_Matrix; procedure Set_Re (X : in out Complex_Matrix; Re : Real_Matrix); procedure Set_Im (X : in out Complex_Matrix; Im : Real_Matrix); function Compose_From_Cartesian (Re : Real_Matrix) return Complex_Matrix; function Compose_From_Cartesian (Re, Im : Real_Matrix) return Complex_Matrix; function Modulus (X : Complex_Matrix) return Real_Matrix; function "abs" (Right : Complex_Matrix) return Real_Matrix renames Modulus; function Argument (X : Complex_Matrix) return Real_Matrix; function Argument (X : Complex_Matrix; Cycle : Real'Base) return Real_Matrix; function Compose_From_Polar (Modulus, Argument : Real_Matrix) return Complex_Matrix; function Compose_From_Polar (Modulus : Real_Matrix; Argument : Real_Matrix; Cycle : Real'Base) return Complex_Matrix; -- Complex_Matrix arithmetic operations function "+" (Right : Complex_Matrix) return Complex_Matrix; function "-" (Right : Complex_Matrix) return Complex_Matrix; function Conjugate (X : Complex_Matrix) return Complex_Matrix; function Transpose (X : Complex_Matrix) return Complex_Matrix; function "+" (Left, Right : Complex_Matrix) return Complex_Matrix; function "-" (Left, Right : Complex_Matrix) return Complex_Matrix; function "*" (Left, Right : Complex_Matrix) return Complex_Matrix; function "*" (Left, Right : Complex_Vector) return Complex_Matrix; function "*" (Left : Complex_Vector; Right : Complex_Matrix) return Complex_Vector; function "*" (Left : Complex_Matrix; Right : Complex_Vector) return Complex_Vector; -- Mixed Real_Matrix and Complex_Matrix arithmetic operations function "+" (Left : Real_Matrix; Right : Complex_Matrix) return Complex_Matrix; function "+" (Left : Complex_Matrix; Right : Real_Matrix) return Complex_Matrix; function "-" (Left : Real_Matrix; Right : Complex_Matrix) return Complex_Matrix; function "-" (Left : Complex_Matrix; Right : Real_Matrix) return Complex_Matrix; function "*" (Left : Real_Matrix; Right : Complex_Matrix) return Complex_Matrix; function "*" (Left : Complex_Matrix; Right : Real_Matrix) return Complex_Matrix; function "*" (Left : Real_Vector; Right : Complex_Vector) return Complex_Matrix; function "*" (Left : Complex_Vector; Right : Real_Vector) return Complex_Matrix; function "*" (Left : Real_Vector; Right : Complex_Matrix) return Complex_Vector; function "*" (Left : Complex_Vector; Right : Real_Matrix) return Complex_Vector; function "*" (Left : Real_Matrix; Right : Complex_Vector) return Complex_Vector; function "*" (Left : Complex_Matrix; Right : Real_Vector) return Complex_Vector; -- Complex_Matrix scaling operations function "*" (Left : Complex; Right : Complex_Matrix) return Complex_Matrix; function "*" (Left : Complex_Matrix; Right : Complex) return Complex_Matrix; function "/" (Left : Complex_Matrix; Right : Complex) return Complex_Matrix; function "*" (Left : Real'Base; Right : Complex_Matrix) return Complex_Matrix; function "*" (Left : Complex_Matrix; Right : Real'Base) return Complex_Matrix; function "/" (Left : Complex_Matrix; Right : Real'Base) return Complex_Matrix; -- Complex_Matrix inversion and related operations function Solve (A : Complex_Matrix; X : Complex_Vector) return Complex_Vector; function Solve (A, X : Complex_Matrix) return Complex_Matrix; function Inverse (A : Complex_Matrix) return Complex_Matrix; function Determinant (A : Complex_Matrix) return Complex; -- Eigenvalues and vectors of a Hermitian matrix function Eigenvalues (A : Complex_Matrix) return Real_Vector; procedure Eigensystem (A : Complex_Matrix; Values : out Real_Vector; Vectors : out Complex_Matrix); -- Other Complex_Matrix operations function Unit_Matrix (Order : Positive; First_1, First_2 : Integer := 1) return Complex_Matrix; end Ada.Numerics.Generic_Complex_Arrays;